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Annals of Global Analysis and Geometry

, Volume 46, Issue 3, pp 227–239 | Cite as

Flat fronts in hyperbolic 3-space with prescribed singularities

  • Antonio Martínez
  • Francisco MilánEmail author
Article

Abstract

The paper deals with the study of flat fronts in the hyperbolic 3-space, \(\mathbb {H}^3\). We characterize when an analytic curve of \(\mathbb {H}^3\) is in the singular set of some flat front with prescribed cuspidal edges and swallowtail singularities. We also prove that every complete flat front with a non-degenerate analytic planar singular set must be rotational.

Keywords

Hyperbolic 3-space Flat fronts Cuspidal edges  Swallowtails 

Mathematical Subject Classification (2000)

53A35 53C42 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Departamento de Geometría y TopologíaUniversidad de GranadaGranadaSpain

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